Question:
How could we tell someone on the other side of the world where we want to meet them for coffee?
It depends on how we talk about the world.
Thankfully, we can communicate mathematically.
Well it's not flat.
The earth actually isn't even a perfect sphere,
especially given the topographic changes of mountain ranges and valleys.
We call the shape of the Earth a spheroid.
A sphereoid is defined by:
And there are many approximations (meters):
A datum is built on top of the selected spheroid and can incorporate local variations in elevation.
Basically, we are setting the origin of our sphere as if it were placed on the earths actual geoid.
For example: Bellingham, WA
| Datum | Longitude | Latitude |
|---|---|---|
| NAD 1927 | -122.46690368652 | 48.7440490722656 |
| NAD 1983 | -122.46818353793 | 48.7438798543649 |
| WGS 1984 | -122.46818353793 | 48.7438798534299 |
Break down a sphere into:
Origins on the Earth:
Together form: Graticule
Both of these are measurements from the Earth's center to a point of the Earth's surface.
These two allow us to find any place on Earth.
Cool!!! And it's called:
What is this actually measuring...?
Units:
Unit Equivalencies
$$1° = 60' = 3600"$$
$$1' = (\frac{1}{60})° = 0.01666667°$$
$$1" = (\frac{1}{3600})° = 2.77778e^{-4}° = 0.000277778°$$
Well what does that mean...?
Described as a Coordinate Pair: (x,y) <- (in most cases)
Decimal Degrees:
Sexagesimal
DM -> DD:
$$decimal degrees = degrees + \frac{Minutes}{60} + \frac{seconds}{3600}$$DD -> DM:
$$absdd = |dd|$$
$$degrees = integer(absdd)$$
$$minutes = integer((absdd - degrees) * 60)$$
$$seconds = ((absdd - degrees - \frac{minutes}{60}) * 3600)$$
1 degree of longitude at the equator: 111.321 KM
1 degree of longitude at 60 degrees of latitue: 55.802 KM
Woah, thats weird...
UTM Zone 10 (FT)
WA State Plane South (FT):
We can use different types of math here to be able to flatten the sphere to a 2d plane.
Different projection formulas result in different types of projections.
Additionally, different projection formulas can be used to preserve angles, area, or distance.
The four spatial properties that are subject to distortion are: shape, area, distance and direction
Shape, angle, scale may all be distorted. Graticules may not intersect at right angles.
Scale is only preserved in some areas of a map.
Each map projection is good at preserving only one or two of the four spatial properties.
So when working with small-scale (large area) maps and when multiple spatial properties are to be preserved, it is best to break the analyses across different projections to minimize errors associated with spatial distortion.
Projected coordinate systems will introduce errors in measurements.
This is due to the difference in computing the distance between two points. On a sphere, the distance traveled is in an arc, but in a planar coordinate system, typically a linear system.
Distance between two points in a planar system:
Point(4, 1)
Point(5, 6)
A geodesic distance is the shortest distance between two points on an ellipsoid (or spheroid).
A geodesic area measurement is one that is measured on an ellipsoid.
Most of the time, the scales we are producing maps at allow us to ignore these errors, as the levels of tolerance in our calculations allow for such precision.
However, if we use small scale analysis (covering a large area of the earth), then often these levels of precision are exceeded.
Two standard parallels
Commonly used for maps of the conterminous United States.
<cartopy.mpl.gridliner.Gridliner at 0x126b0b340>
Directions, angles, and shapes are maintained at infinitesimal scale.
<cartopy.mpl.gridliner.Gridliner at 0x126f25ee0>
The meridians and parallels are equally spaced straight lines forming a Cartesian grid.
Each rectangular grid cell has the same size, shape, and area only in the projected space.
<cartopy.mpl.gridliner.Gridliner at 0x126f9fa30>
<cartopy.mpl.gridliner.Gridliner at 0x127a94490>
Used for mapping large-scale or smaller areas with predominantly north-south trending extents.
Conformal map projection
<cartopy.mpl.feature_artist.FeatureArtist at 0x127b33100>
The UTM system divides the Earth into 60 zones, each 6° of longitude in width.
| UTM Zone | Central Meridian | UTM Zone Extent |
|---|---|---|
| 10 | 123°W | 126°W-120°W |
State Plane system of large-scale conformal map projections originally created in the 1930s to support surveying, engineering, and mapping activities throughout the U.S. and it's territories.

Loosely based on:
Problems - Puget Sound Metro
King County: "Washington State Plane North"
Pierce County: "Washington State Plane South"
I have even encountered a custom projection to deal with this issue!!
There are a variety of different projections for different reasons and I don't expect you to know them all.
However, you will need to know how to find a projection of a data source, map, and other services to be able to work with data.
Each agency typically has their own standards and you will be asked to use that when working with that data.
Learning ArcGIS Pro 2: Chapter 3